Math Snap

STEP 1

1. We are dealing with a right triangle.
2. We are given one angle $33^\circ$ and one side $23$ m.
3. We need to find the length of the side designated by the lowercase letter $c$.
4. The side $c$ is opposite the given angle $33^\circ$.

STEP 2

1. Identify the known elements of the triangle.
2. Use trigonometric ratios to find the unknown side.
3. Solve for the side $c$.

STEP 3

Identify the known elements of the triangle:
- The angle $A = 33^\circ$.
- The side adjacent to angle $A$, which is $23$ m.
- The side opposite angle $A$ is designated by the lowercase letter $c$.

STEP 4

Use the tangent trigonometric ratio, which relates the opposite side to the adjacent side in a right triangle:
$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ For this triangle:
$$\tan(33^\circ) = \frac{c}{23}$$

STEP 5

Solve for the side $c$:
$$c = 23 \cdot \tan(33^\circ)$$

Calculate the value of $c$ using a calculator:
1. Find $\tan(33^\circ)$ using a calculator.
2. Multiply the result by $23$.
$$c \approx 23 \cdot 0.6494$$ $$c \approx 14.9362$$ The measure of the side $c$ is approximately $14.94$ meters.